00:01
Hi, i'm david and i'm here to help you answering your question.
00:03
Let me bring up your question here.
00:05
In this question we discuss about the normal distribution, where we are given the x followed by the normal with the mean equal to 859, standard deviation equal to the 50.
00:19
Now recall to you that if we turn the x minus the mean divided by standard deviation, you will follow by the standard normal.
00:26
Now in the part a, we want to find the 1 % of the student score between 80.
00:35
So, i want to find probability of the x between 820 and 934.
00:43
Now with first step, we need to turn the x into the z.
00:47
So we need to take the value 820 minus the mean will be 859, divided by the standard division will be 50.
00:56
We do the same thing on the right, minus 5, 59, divided by 50.
01:03
And if we do the calculation here, we get equal to probability under z between the value a20 minus a59, divided by 50, can equal to the minus 0 .7, 8.
01:20
On the right, we have 934 minus 8.
01:25
59 divided by 50 equal to the 1 .5.
01:30
Now this probability in turn can be written as a total probability minus the one on the left will be the smaller than minus 0 .78 minus the one on the right but because of the symmetry we will put the minus 1 .5 here.
01:48
And now to compute this probability i need to bring up the z table.
01:52
So let me complete the z table for you and then i will show you.
01:55
You have to use it.
01:59
So i will put the table here.
02:06
Now look at the table, we want to have the equal to 1 minus.
02:11
Here for this we have the minus 0 .7 here, 8 here.
02:17
So we have the value equal to 0 .277.
02:22
For this one, minus 1 .5, be here.
02:26
So we have the value will be minus 0 .0668.
02:30
And if we do the calculation, we have 1 minus 0 .2, 177 minus 0 .06 68, can equal to 0 .7 -155.
02:44
And this will be the answer for the a.
02:46
Now for the b, once you find the probability that the student got 942 or more.
02:53
So probability x greater than 942...